SAMPLE SURVEYS Objective: How do we find out information about populations using samples? HOMEWORK: On pages , READ SECTION 5-1 (really read it!) and complete exercises 5.5, 5.7, 5.10, 5.13, 5.15 ESP TASK IS DUE FRIDAY

Populations vs. Samples Population – the entire group of individuals we would like to find information about. Sample – a smaller group of individuals selected from the population

Suppose you have created a survey that you want to give to the high school population. You obviously can’t give it out to every single student in the school – that would take too much time and work. How could you select a sample to survey?

Class Ideas Ask a teacher to hand out randomly to their students – range in age, intelligence, ethnicity and gender Anonymous Announcement – “who wants to take the survey” – come get it Give out to every 10 th person you see

Methods of selecting a sample of students to give out a survey to: Give the survey to people who enter our school Post questions on facebook Give to your friends Distribute them to as many people as possible Give during a class period - have a box for students to put their responses in Give during lunch and have students return it right after Give out 150 copies and have students return personally to me.

More methods Give to 5 random classes in the morning and 5 random ones in the afternoon Interview random people during lunch or free periods Give to the first 20 people I see in fresh/soph. gym class and the first 20 people in a junior/senior gym class.

Simple Random Sample How do we conduct an SRS? How can we use what we know about simulation to make sure that the students we select for our sample are random? Why is it important that our sample be random?

In random sampling, Chance rather than human choice is being used to select a sample Remember when everyone in our class except for 4 people “randomly” chose #3? Let’s test our ability to pick representative “people” or groups for our sample…

Random Rectangles DO NOT TURN OVER THE SHEET UNTIL I TELL YOU TO DO SO 6.75, 9, 5, 6, 10, 7.5, 10, 8, 4, 7, 9.2

Estimate the average area of the rectangles on this sheet. For example, rectangle 33 has an area 4 x 3 = 12. Write down your estimate. You have 5 seconds.

Now select 5 rectangles that in your judgment, are representative of the rectangles on the page. Write down the area for each of the 5. Compute the average of the five areas and compare it with your estimate. Are the two numbers close? Let’s collect data from the class and draw dotplots of our initial estimates and histograms or dotplots of our average of five areas.

Random Samples Now use a random number table or random number generator to select five distinct random numbers between 00 and 99. Find the five rectangles with these numbers and mark them on the sheet. This is your random sample of 5 rectangles. Compute the areas of these 5 sampled rectangles and find the average. How does this average compare with your earlier estimates? Let’s make another histogram or dot plot for this data.

Rand Int (01, 100, 5) Random Areas: 6, 13.6, 8.4, 12.4, 8.4, 11.6, 10, 7.8, 7.8, 3.6, 4.8

Data Analysis Calculate the mean and standard deviation of all the sample averages for the subjective sample and for the random sample. How do the centers and spreads of these distributions compare?

BIAS Sampling methods that tend to over or under emphasize some characteristics of the population are said to be biased.